Combinatorial Reallocation Mechanisms

Liad Blumrosen*, Shahar Dobzinski

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We consider reallocation problems in settings where the initial endowment of each agent consists of a subset of the resources. The private information of the players is their value for every possible subset of the resources. The goal is to redistribute resources among agents to maximize efficiency. Monetary transfers are allowed, but participation is voluntary. We develop incentive-compatible, individually-rational and budget-balanced mechanisms for two settings in which agents have complex multi-parameter valuations, both settings include double auctions as a special case. The first setting is combinatorial exchanges, where we provide a mechanism that achieves a logarithmic approximation to the optimal efficiency when valuations are subadditive. The second setting is Arrow–Debreu markets for a single divisible good, where we present a constant approximation mechanism. The first result is given for a Bayesian setting, where the latter result is for prior-free environments.

Original languageAmerican English
JournalAlgorithmica
DOIs
StateAccepted/In press - 2023

Bibliographical note

Publisher Copyright:
© 2023, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.

Keywords

  • Budget balance
  • Combinatorial auctions
  • Double auctions
  • Exchanges
  • Mechanism design
  • Two-sided markets

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